Implications of ANEC for SCFTs in four dimensions

Understand

We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions $\Delta$ of operators in four-dimensional $\mathcal{N}=1$ superconformal field theories.

• We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on $\Delta$.
• We analyze in detail chiral operators in the $(\frac12 j,0)$ Lorentz representation and prove that the ANEC implies the lower bound $\Delta\ge\frac32j$, which is stronger than the corresponding unitarity bound for $j>1$.
• We also derive ANEC bounds on $(\frac12 j,0)$ operators obeying other possible shortening conditions, as well as general $(\frac12 j,0)$ operators not obeying any shortening condition.